## 1. Introduction

The design of aircraft is inherently a multi-disciplinary undertaking, during which data and information must be exchanged between multiple teams of engineers, each with expertise in a specific field. Managing the transmission, possibly translation and storage of data between collaborating groups is complex and error-prone. The adoption of a standardized, data-centric scheme for storage of all data improves consistency and reduces the risk of misconceptions and conflicts. In order to achieve this effectively, an initial effort must be made to develop suitable interfaces between the analysis modules and the data archive.

Furthermore, each phase of the design process poses different requirements on the fidelity and resolution of the design and analysis tools. For stability and control analysis, as well as for flight simulation, look-up tables for aerodynamic forces, moments and derivatives need to be generated. Different flight analysis tools require different tables/input formats. For example, the flight analyzer and simulator PHALANX [

1,

2,

3,

4] developed by Delft University of Technology requires a set of three-dimensional tables of force and moment coefficients with the effect of each control channel acting individually. Multi-fidelity aerodynamic modeling aims to cover the flight state parameter space of the entire flight envelope with an optimal distribution of computational resources. This again requires a standardized, data-centric scheme to host the data, which can be used for variable fidelities.

The label Li , where $i=0,1,2,3$, is used to classify the fidelity level of a computational model and its software implementation:

- L0:
handbook methods, based on statistics and/or empirical design rules;

- L1:
based on simplified physics, can model and capture a limited amount of effects. For example, the linearized-equation models, the Vortex-Lattice Method (VLM) or the panel method in aerodynamics;

- L2:
based on accurate physics representations. For example, the non-linear analysis, Euler-based CFD;

- L3:
represents the highest end simulations, usually used to capture detailed local effects, but do not allow wide exploration of the design space due to computational cost. Additionally, the modeling may require extensive ad hoc manual intervention. For example, the highest fidelity methods, RANS-based CFD.

To construct a reasonable variable fidelity CFD analysis system, one should consider the variable fidelity of the geometrical representations corresponding to the CFD tools. The level of detail in the geometry gathered from a CAD system needs to match the CFD model fidelity. The chosen high fidelity model must be as accurate as possible and can reflect all considered complex flow characteristic; the chosen low-fidelity model must reflect the basic flow characteristics and be as effective as possible. In the conceptual design stage, the usual practice, for example, in the RDS [

5], the AAA [

6] and the VSP [

7] software systems, is to use a purpose-specific CAD that is simpler than the commercial systems, and fewer parameters need to be used for the configuration layout at this stage in the design cycle [

8]. However, for some innovative configurations, different ranges of flight conditions or more detailed analyses, the simplified CAD is not sufficient for a higher fidelity CFD analysis; thus, an enriched geometry definition with more parameters is needed. The Common Parametric Aircraft Configuration Schema (CPACS) [

9,

10], defining the aircraft configuration parametric information in a hierarchical way, gives the opportunity to incorporate different fidelity CFD tools with one single CPACS file. For different fidelity tools to be used, the corresponding geometry information can be imported/retrieved from the common CPACS file to match the model fidelity.

SUAVE, Standford University Aerospace Vehicle Environment [

11,

12,

13], which is also a multi-fidelity design framework developed at Stanford University, stores the aircraft geometry information using an inherent defined data class, which can be easily modified. The aerodynamic solutions can be generated from simple models within SUAVE or easily imported from external sources like CFD or wind tunnel results. The aircraft analysis in SUAVE is calculated with a so-called “fidelity zero” VLM to predict lift and drag, with a number of corrections such as the compressibility drag correction, parasite drag correction, etc. [

12], to adapt the VLM prediction to a wider range (transonic and supersonic flow regions). It incorporates the “multi-fidelity” aerodynamics through the provided response surface by combining the different fidelity data. However, currently, SUAVE is still working on connecting higher fidelity models directly to it; the response surfaces are only available to incorporate higher fidelity lift and drag data from the external sources [

12]. At this point, one cannot guarantee that the geometry information used for different fidelity tools is consistent during data exchanging, transferring and translating. Moreover, the prediction is only limited to lift and drag, so that it might not be easy for engineers to look into the physical details for a better design, for example, the pressure isobars and distributions, the laminar flows, transitions and the shock forming, etc. Thus, a dataset that can store complete and consistent information for different fidelity tools to solve the physical flows is desired. The CPACS-based multi-fidelity aerodynamic tools show a great consistency due to the one data-centric schema, and the automation of the progressive process can thus be implemented and realized with minimum data loss.

With all the computed aerodynamic data at hand, an important task is to construct surrogate models that integrate all analysis results computed by tools of different fidelity. Such data fusion applications are enabled by standardization of the data—format, syntax and semantics—of the aerodynamic simulation tools. The work in [

14] describes the workflow of an automatic data fusion process for CPACS [

9,

10]. The application was developed in the EU research project Aircraft 3rd Generation MDO for Innovative Collaboration of Heterogeneous Teams of Experts (AGILE) [

15], where every module (the aerodynamic module, the sampling module, the surrogate modeling module) communicates by CPACS files.

This paper will address other aspects of the work in [

14], namely how the different fidelity tools in the aerodynamic module communicate and how a look-up table of the aero-dataset can be obtained automatically from the tools (L1 and L2 in this paper).

Section 2 describes the CPACS file definition in more detail, especially the geometry definitions, which are important for CFD mesh generators.

Section 3 details the CPACS interfaces for variable fidelity analysis.

Section 4 gives an overview of the CFD flow solvers used in the work.

Section 5 presents the applications to the test case using variable fidelity tools.

Section 6 discusses different modeling approaches for control surfaces used for Euler simulations, and finally,

Section 7 summarizes the conclusions of the work.

#### 1.1. Background

AGILE is an EU-funded Horizon 2020 project coordinated by the Institute of Air Transportation Systems of the German Aerospace Center (DLR). Its objective is to implement a third generation multidisciplinary optimization process through efficient collaboration by international multi-site design teams. The 19 partners bring different knowledge and competences regarding aircraft design and optimization. As mentioned above, such a collaboration is enabled by the adoption of a common data storage format. To this end, AGILE relies on the XML format CPACS (Common Parametric Aircraft Configuration Schema) [

9,

10] in development at DLR since 2005.

The RCE (Remote Component Environment) integration environment and workflow manager [

16] controls and executes the sequence of analysis modules and manages the data transport and translation, as well as logging the process. RCE makes it easy to set up an MDO workflow also with modules running on remote hosts. That is handled by the BRICS (Building blocks for mastering network Restrictions involved in Inter-organisational Collaborative engineering Solutions) [

17] system, which supports remote execution and data transport. The request can be with “engineer in the loop” for a remote expert to run the calculation or for an automated workflow to be run without user intervention. The input is generally a CPACS file containing all the information required. The new data generated are added to the CPACS file and sent back to the requester. More details about the AGILE collaborative approach can be found in [

18,

19].

The variable fidelity aerodynamic tools read a CPACS file, analyze the corresponding information extracted from the file, run the calculation and store the new data (e.g., aero-data tables) back to the CPACS file. CPACS supports a very flexible user-defined node feature (

`cpacs.toolspecific`) to handle parameters for the computational models, which are relevant only for a specific tool [

20].

#### 1.2. Aerodynamic Model Description

The test case is the reference aircraft used in AGILE, a regional jet-liner, which was analyzed and simulated using the AGILE MDO system, without experimental data. This virtual aircraft is similar to an Airbus 320 or a Boeing 737. The reference aircraft is defined in CPACS [

9] format, shown in

Figure 1. Its aspect ratio is 9.5, and the detailed information of the airfoils along the aircraft span is shown in

Figure 2.

Figure 2a shows the plots of the airfoil along the three stations of the semi-span (

$b/2$), with the root at 0%, the kink at 40% and the tip at 100%.

Figure 2b shows the maximum thickness and cambers per chord along the semi-span, as well as the corresponding locations of the local chords. It should be noted that the design exercises are carried out as if in an early design stage, so for instance, no engine is modeled. The configuration was also used in previous studies, to benchmark the conceptual design software CEASIOM [

20] and to validate the AGILE data fusion tool [

14] for building multi-fidelity aero-datasets. Some of the results shown in this paper are consistent with the previous simulations in [

14,

20], that the configuration is unchanged and the same CPACS file for geometry definition is used to assure a consistent and continuous investigation of the tools and methods.

## 4. Flow Solvers

The CFD (fidelity level L2–3) codes SU2 [

29,

31] and Edge [

28] are used for Euler and RANS flow modeling.

Edge is the Swedish national CFD code for external steady and unsteady compressible flows. Developed by the Swedish Defense Research Agency (FOI), it uses unstructured grids with arbitrary elements and an edge-based formulation with a node-centered finite-volume technique to solve the governing equations. Edge supports a number of turbulence models, as well as LES and DES simulations.

The SU2 [

29] software suite from Stanford University is an open-source, integrated analysis and design tool for complex, multi-disciplinary problems on unstructured computational grids. The built-in optimizer is a Sequential Least Squares Programming (SLSQP) algorithm [

32] from the SciPy Python scientific library. The gradient is calculated by continuous adjoint equations of the flow equations [

29,

31]. SU2 is in continued development. Most examples pertain to inviscid flow, but also, RANS flow models with the Spalart–Allmaras and the Menter’s Shear Stress Transport (SST)

$k-\omega $ turbulence models can be treated.

Figure 12 shows the comparison of the aerodynamic coefficients computed by Euler equations in SU2 and Edge for two different meshes of the reference aircraft. “Mesh-4p” has 4.0 million cells, and “mesh-2p” has 1.9 million cells. The meshes have the same meshing parameter settings as described in [

20]. Both have refined wing leading and trailing edges, and “mesh-4p” has settings for even smaller minimum dimensions of the cells. According to the mesh study in [

20], the predictions from both solvers converge as the mesh resolution increases, and “mesh-4p” was selected in [

20] for all the simulations carried out by SU2 by considering both computational accuracy and efficiency. In this paper, more simulations are made for both “mesh-2p” and “mesh-4p” using both Edge and SU2 for different flight conditions. For “mesh-2p”, Edge and SU2 give fairly close predictions for the aerodynamic coefficients

${C}_{L}$,

${C}_{D}$ and

${C}_{m}$ at Mach = 0.78 and 0.9. In the current study, we will use “mesh-4p” for the Euler solutions by SU2 in

Section 5 and “mesh-2p” for the calculations on control surface modeling in

Section 6, where SU2 and Edge are used to compare the geometry modeling approaches.

## 5. Applications

#### 5.1. Aerodynamic Results Comparison

The aerodynamic coefficients obtained with L1 and L2 fidelity tools are compared in

Figure 13. A Mach number of 0.6 was used to avoid transonic effects (at low angles of attack) that are not well predicted by L1 (Tornado). The flight condition used for this comparison is an altitude of 5000 m and a side slip angle

$\beta =0$ deg. The L3 (RANS) simulations for a fully-turbulent flow [

33] using the Spalart–Allmaras turbulence model are also shown at the same flight condition, as the highest fidelity data for verification. The RANS mesh is generated by

`Pentagrow` using the same

`Sumo` surface mesh for the L2 Euler computations, which has 792,900 triangles on the surface. The RANS mesh has 8.2 million cells. The first layer height is

$3.8\times {10}^{-6}$ (

${y}^{+}=1$); the growth rate is 1.2; the number of layers is 40, with the corresponding Reynolds number 32.4 million of the reference chord 3.7317 m. The airspeed is 192 m/s, which corresponds to Mach = 0.6 and altitude = 5000 m.

Figure 14 shows the computed

${y}^{+}$ diagram over the reference aircraft at

$\alpha ={1}^{\circ}$ with airspeed 192 m/s and Reynolds number 32.4 million.

Note that the L2 and L3 simulations agree quite well, so that we can safely assume that for this configuration under the corresponding flight conditions, L2 simulations are “as best as” the L3 simulations. In this paper, we only discuss L1 and L2 tools and their simulations. The numerical flow for $\alpha \ge {10}^{\circ}$ is highly unsteady and is not entirely converged, the aerodynamic forces calculated by the L2 and L3 tools are the mean values of the iterations in the search of a steady flow.

The lift coefficient ${C}_{L}$ is well predicted by both L1 and L2 tools between angles of attack of −5${}^{\circ}$ and +5${}^{\circ}$. Above this range, “computational” stall occurs at $\alpha $ of approximately 8${}^{\circ}$, which is clearly visible in the L2 results.

The drag polar shows that the minimum drag coefficient is obtained for an angle of attack of about −2.5${}^{\circ}$ where ${C}_{L}$ vanishes. The minimum ${C}_{D}$ is very small with both Tornado (L1) and SU2 Euler (L2) because they do not include skin friction drag in their physical model and there is no wave drag. The L2 prediction of high ${C}_{D}$ for high angles of attack is due to wave drag. The pitching moment coefficient ${C}_{m}$ on the left corner shows that the aircraft is longitudinally stable ($\partial {C}_{m}/\partial \alpha <0$) for angles of attack from −5${}^{\circ}$ to +5${}^{\circ}$. The breaks in the curves after +5${}^{\circ}$ are different. For L2, it is due to “computational” stall of the horizontal stabilizer. As a reminder, this aircraft is only in the first phase of its design, so it has not been optimized in terms of stability.

The good agreement for some ranges obtained by different fidelity aerodynamic tools supports the idea of building a surrogate model trained by an automatic sampling approach that takes advantage of each method according to their fidelity levels and limitations. For example, it is useless to spend computational time with Euler calculations in the linear aerodynamic region where Tornado can give reliable results. This computational time is better spent on higher Mach number or angles of attack where the cheapest tools fail. An application of the “variable fidelity” technique is to fuse the data from different fidelity levels of tools by kriging and co-kriging [

34]; see also [

14].

#### 5.2. Multi-Fidelity Aerodynamics for Data Fusion

A surrogate model with automatic sampling fuses the data obtained by the different aerodynamic tools. This is useful for constructing a look-up aero-table for quality analysis and flight simulation. This section shows which are the final surrogate models of the static aerodynamic coefficients for horizontal flight, and more results are also shown in [

14]. The aircraft handling qualities are also predicted and analyzed; see the details in [

14]. The multi-fidelity of the aerodynamic tools used to generate the various data for constructing the surrogate models is executed via BRICS remotely at different sites by importing/exporting the common CPACS file through the interfaces described in this paper.

Figure 15 shows the fused

${C}_{L}$,

${C}_{D}$ and

${C}_{m}$ aero-coefficient results of the reference aircraft model from the L1 Tornado) and L2 SU2 Euler tools with the elevator deflection

$\delta ={0}^{\circ}$ over the flight envelope. • represents the Tornado samples, and × represents the SU2 Euler samples.

Figure 15a,c,e shows the response surfaces from the surrogate models, as well as the sampled data over the flight envelope in the three-dimensional space.

Figure 15b,d,f represents the variation with

$\alpha $ and

${\delta}_{e}$ for Mach numbers 0.5 (black) and 0.78 (blue) from the response surfaces and their corresponding sampled data.

Figure 15a,b shows the surrogate models (response surfaces) for

${C}_{L}$ produced by co-kriging [

34]. The non-linear behavior at higher angles of attack is captured as the L2 samples indicate.

Figure 15c,d shows the prediction for

${C}_{D}$. The surrogate model predicts higher drag than the L1 samples, since they do not predict wave drag. The surrogate model picks up the compressibility phenomena from the L2 samples.

The surrogate model for

${C}_{m}$ is shown in

Figure 15e,f. Note again that the surrogate model predicts the non-linear trends at high AoA, as expected. The coarse L2 samples correct the response surfaces significantly.

The computation time of the surrogate model is ≈0.05 s on a desktop computer with four CPUs. The reliability of the surrogate as indicated by the root mean square error $max\left(\mathrm{RMSE}\right)=0.048<5\%$.

#### 5.3. Aero-Data for Low Speed by the L1 Tool

Tornado computes all static and quasi-static aerodynamic coefficients, including the effects of trailing edge device deflections. In the following paragraphs, the sizing of the rudder and horizontal trim and handling qualities are discussed based on the Tornado calculations.

#### 5.3.1. Sizing the Fin and Rudder for the One-Engine-Out Case

An aircraft must have an established minimum control speed

${V}_{MC}$, legally defined in, e.g., [

35], as the lowest calibrated airspeed at which the aircraft is controllable. It may not be larger than 1.13-times the reference stall speed. Aircraft with engines set far from the centerline will experience large yawing moments if an engine fails. The sizing of the vertical tail, and its rudder, is usually determined by a one-engine-out case. Flying with side-slip and rudder deflection, at a certain airspeed, the fin and rudder produce just enough yawing moment to counteract the asymmetric thrust. This speed is essentially the minimum control speed, although certification requires a few more parameters.

In this section, an exercise of sizing the rudder of the aircraft is carried out by Tornado, using a simplified method as described by Torenbeek [

36]. Side-slip and roll response were neglected, and the tail volume [

37] was held constant.

As an initial estimate, the minimum control speed for different control surface sizes was computed until the requirement of 1.13 of the stall speed was achieved. The selected rudder deflection was 25 degrees to allow five degrees of maneuver margin.

Figure 16 shows the predicted minimum control velocity.

#### 5.3.2. Handling Qualities

The horizontal sea level trim at low speed can be estimated from the aero-coefficients and the mass distribution whose reference values are available from CPACS. The straight and level flight trim results at sea level, calculated by Tornado in [

20] are shown in

Figure 17.

The classical modes of motion indicate the linear stability of the aircraft, i.e., its responses to (infinitesimally) small disturbances. Flight simulation allows the full range of stability of the aircraft to be assessed. The time history in

Figure 18 shows how the attitude angle

$\theta $, the angle of attack

$\alpha $ and the pitch rate

q oscillate when excited by a step-function-type elevator movement. The PHALANX [

1,

2,

3,

4,

38], a flight simulation tool from Delft University of Technology, produced the time histories.

The time domain simulation starts as trimmed straight and level flight at sea level conditions with True Air Speed 130 m/s. After 1 s, the pilot executes a 2-3-1-1 maneuver in pitch, namely, stick 2 s nose down, 3 s nose up, 1 s nose down and 1 s nose up.